<html><!-- Created using the cpp_pretty_printer from the dlib C++ library.  See http://dlib.net for updates. --><head><title>dlib C++ Library - point_transforms_abstract.h</title></head><body bgcolor='white'><pre>
<font color='#009900'>// Copyright (C) 2003  Davis E. King (davis@dlib.net)
</font><font color='#009900'>// License: Boost Software License   See LICENSE.txt for the full license.
</font><font color='#0000FF'>#undef</font> DLIB_POINT_TrANSFORMS_ABSTRACT_Hh_
<font color='#0000FF'>#ifdef</font> DLIB_POINT_TrANSFORMS_ABSTRACT_Hh_

<font color='#0000FF'>#include</font> "<a style='text-decoration:none' href='../matrix/matrix_abstract.h.html'>../matrix/matrix_abstract.h</a>"
<font color='#0000FF'>#include</font> "<a style='text-decoration:none' href='vector_abstract.h.html'>vector_abstract.h</a>"
<font color='#0000FF'>#include</font> "<a style='text-decoration:none' href='rectangle_abstract.h.html'>rectangle_abstract.h</a>"
<font color='#0000FF'>#include</font> "<a style='text-decoration:none' href='drectangle_abstract.h.html'>drectangle_abstract.h</a>"
<font color='#0000FF'>#include</font> <font color='#5555FF'>&lt;</font>vector<font color='#5555FF'>&gt;</font>

<font color='#0000FF'>namespace</font> dlib
<b>{</b>

<font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
    <font color='#0000FF'>class</font> <b><a name='point_transform_affine'></a>point_transform_affine</b>
    <b>{</b>
        <font color='#009900'>/*!
            WHAT THIS OBJECT REPRESENTS
                This is an object that takes 2D points or vectors and 
                applies an affine transformation to them.

            THREAD SAFETY
                It is safe for multiple threads to make concurrent accesses to this object
                without synchronization.
        !*/</font>
    <font color='#0000FF'>public</font>:

        <b><a name='point_transform_affine'></a>point_transform_affine</b> <font face='Lucida Console'>(</font>
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            ensures
                - This object will perform the identity transform.  That is, given a point
                  as input it will return the same point as output.
        !*/</font>

        <b><a name='point_transform_affine'></a>point_transform_affine</b> <font face='Lucida Console'>(</font>
            <font color='#0000FF'>const</font> matrix<font color='#5555FF'>&lt;</font><font color='#0000FF'><u>double</u></font>,<font color='#979000'>2</font>,<font color='#979000'>2</font><font color='#5555FF'>&gt;</font><font color='#5555FF'>&amp;</font> m,
            <font color='#0000FF'>const</font> dlib::vector<font color='#5555FF'>&lt;</font><font color='#0000FF'><u>double</u></font>,<font color='#979000'>2</font><font color='#5555FF'>&gt;</font><font color='#5555FF'>&amp;</font> b
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            ensures
                - #get_m() == m
                - #get_b() == b
                - When (*this)(p) is invoked it will return a point P such that:
                    - P == m*p + b
        !*/</font>

        <font color='#0000FF'>const</font> dlib::vector<font color='#5555FF'>&lt;</font><font color='#0000FF'><u>double</u></font>,<font color='#979000'>2</font><font color='#5555FF'>&gt;</font> <b><a name='operator'></a>operator</b><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font> <font face='Lucida Console'>(</font>
            <font color='#0000FF'>const</font> dlib::vector<font color='#5555FF'>&lt;</font><font color='#0000FF'><u>double</u></font>,<font color='#979000'>2</font><font color='#5555FF'>&gt;</font><font color='#5555FF'>&amp;</font> p
        <font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>;
        <font color='#009900'>/*!
            ensures
                - applies the affine transformation defined by this object's constructor
                  to p and returns the result.
        !*/</font>

        <font color='#0000FF'>const</font> matrix<font color='#5555FF'>&lt;</font><font color='#0000FF'><u>double</u></font>,<font color='#979000'>2</font>,<font color='#979000'>2</font><font color='#5555FF'>&gt;</font><font color='#5555FF'>&amp;</font> <b><a name='get_m'></a>get_m</b><font face='Lucida Console'>(</font>
        <font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>;
        <font color='#009900'>/*!
            ensures
                - returns the transformation matrix used by this object.
        !*/</font>

        <font color='#0000FF'>const</font> dlib::vector<font color='#5555FF'>&lt;</font><font color='#0000FF'><u>double</u></font>,<font color='#979000'>2</font><font color='#5555FF'>&gt;</font><font color='#5555FF'>&amp;</font> <b><a name='get_b'></a>get_b</b><font face='Lucida Console'>(</font>
        <font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>;
        <font color='#009900'>/*!
            ensures
                - returns the offset vector used by this object.
        !*/</font>

    <b>}</b>;

    <font color='#0000FF'><u>void</u></font> <b><a name='serialize'></a>serialize</b>   <font face='Lucida Console'>(</font><font color='#0000FF'>const</font> point_transform_affine<font color='#5555FF'>&amp;</font> item, std::ostream<font color='#5555FF'>&amp;</font> out<font face='Lucida Console'>)</font>;
    <font color='#0000FF'><u>void</u></font> <b><a name='deserialize'></a>deserialize</b> <font face='Lucida Console'>(</font>point_transform_affine<font color='#5555FF'>&amp;</font> item, std::istream<font color='#5555FF'>&amp;</font> in<font face='Lucida Console'>)</font>;
    <font color='#009900'>/*!
        provides serialization support
    !*/</font>

<font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
    point_transform_affine <b><a name='operator'></a>operator</b><font color='#5555FF'>*</font> <font face='Lucida Console'>(</font>
        <font color='#0000FF'>const</font> point_transform_affine<font color='#5555FF'>&amp;</font> lhs,
        <font color='#0000FF'>const</font> point_transform_affine<font color='#5555FF'>&amp;</font> rhs
    <font face='Lucida Console'>)</font>;
    <font color='#009900'>/*!
        ensures
            - returns a transformation TFORM(x) that is equivalent to lhs(rhs(x)).  That
              is, for all valid x: TFORM(x) == lhs(rhs(x)).
    !*/</font>

    <font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
    point_transform_affine <b><a name='inv'></a>inv</b> <font face='Lucida Console'>(</font>
        <font color='#0000FF'>const</font> point_transform_affine<font color='#5555FF'>&amp;</font> trans
    <font face='Lucida Console'>)</font>;
    <font color='#009900'>/*!
        ensures
            - If trans is an invertible transformation then this function returns a new
              transformation that is the inverse of trans. 
    !*/</font>

<font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
    <font color='#0000FF'>template</font> <font color='#5555FF'>&lt;</font><font color='#0000FF'>typename</font> T<font color='#5555FF'>&gt;</font>
    point_transform_affine <b><a name='find_affine_transform'></a>find_affine_transform</b> <font face='Lucida Console'>(</font>
        <font color='#0000FF'>const</font> std::vector<font color='#5555FF'>&lt;</font>dlib::vector<font color='#5555FF'>&lt;</font>T,<font color='#979000'>2</font><font color='#5555FF'>&gt;</font> <font color='#5555FF'>&gt;</font><font color='#5555FF'>&amp;</font> from_points,
        <font color='#0000FF'>const</font> std::vector<font color='#5555FF'>&lt;</font>dlib::vector<font color='#5555FF'>&lt;</font>T,<font color='#979000'>2</font><font color='#5555FF'>&gt;</font> <font color='#5555FF'>&gt;</font><font color='#5555FF'>&amp;</font> to_points
    <font face='Lucida Console'>)</font>;
    <font color='#009900'>/*!
        requires
            - from_points.size() == to_points.size()
            - from_points.size() &gt;= 3
        ensures
            - returns a point_transform_affine object, T, such that for all valid i:
                length(T(from_points[i]) - to_points[i])
              is minimized as often as possible.  That is, this function finds the affine
              transform that maps points in from_points to points in to_points.  If no
              affine transform exists which performs this mapping exactly then the one
              which minimizes the mean squared error is selected.  Additionally, if many
              equally good transformations exist, then the transformation with the smallest
              squared parameters is selected (i.e. if you wrote the transformation as a
              matrix then we say we select the transform with minimum Frobenius norm among
              all possible solutions).
    !*/</font>

<font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
    <font color='#0000FF'>template</font> <font color='#5555FF'>&lt;</font><font color='#0000FF'>typename</font> T<font color='#5555FF'>&gt;</font>
    point_transform_affine <b><a name='find_similarity_transform'></a>find_similarity_transform</b> <font face='Lucida Console'>(</font>
        <font color='#0000FF'>const</font> std::vector<font color='#5555FF'>&lt;</font>dlib::vector<font color='#5555FF'>&lt;</font>T,<font color='#979000'>2</font><font color='#5555FF'>&gt;</font> <font color='#5555FF'>&gt;</font><font color='#5555FF'>&amp;</font> from_points,
        <font color='#0000FF'>const</font> std::vector<font color='#5555FF'>&lt;</font>dlib::vector<font color='#5555FF'>&lt;</font>T,<font color='#979000'>2</font><font color='#5555FF'>&gt;</font> <font color='#5555FF'>&gt;</font><font color='#5555FF'>&amp;</font> to_points
    <font face='Lucida Console'>)</font>;
    <font color='#009900'>/*!
        requires
            - from_points.size() == to_points.size()
            - from_points.size() &gt;= 2
        ensures
            - This function is just like find_affine_transform() except it finds the best
              similarity transform instead of a full affine transform.  This means that it
              optimizes over only the space of rotations, scale changes, and translations.
              So for example, if you mapped the 3 vertices of a triangle through a
              similarity transform then the output would still be the same triangle.
              However, the triangle itself may be larger or smaller, rotated, or at a
              different location in the coordinate system.  This is not the case for a
              general affine transform which can stretch points in ways that cause, for
              example, an equilateral triangle to turn into an isosceles triangle.
    !*/</font>

<font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
    <font color='#0000FF'>class</font> <b><a name='rectangle_transform'></a>rectangle_transform</b>
    <b>{</b>
        <font color='#009900'>/*!
            WHAT THIS OBJECT REPRESENTS
                This object is just a point_transform_affine wrapped up so that it can
                transform rectangle objects.  It will take a rectangle and transform it
                according to an affine transformation.  

            THREAD SAFETY
                It is safe for multiple threads to make concurrent accesses to this object
                without synchronization.
        !*/</font>
    <font color='#0000FF'>public</font>:

        <b><a name='rectangle_transform'></a>rectangle_transform</b> <font face='Lucida Console'>(</font>
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            ensures
                - This object will perform the identity transform.  That is, given a rectangle 
                  as input it will return the same rectangle as output.
        !*/</font>

        <b><a name='rectangle_transform'></a>rectangle_transform</b> <font face='Lucida Console'>(</font>
            <font color='#0000FF'>const</font> point_transform_affine<font color='#5555FF'>&amp;</font> tform
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            ensures
                - #get_tform() == tform
        !*/</font>

        drectangle <b><a name='operator'></a>operator</b><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font> <font face='Lucida Console'>(</font>
            <font color='#0000FF'>const</font> drectangle<font color='#5555FF'>&amp;</font> r
        <font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>;
        <font color='#009900'>/*!
            ensures
                - Applies the transformation get_tform() to r and returns the resulting
                  rectangle.  If the transformation doesn't have any rotation then the
                  transformation simply maps the corners of the rectangle according to
                  get_tform() and returns the exact result.  However, since
                  dlib::drectangle can't represent rotated rectangles, if there is any
                  rotation in the affine transform we will attempt to produce the most
                  faithful possible outputs by ensuring the output rectangle has the
                  correct center point and that its area and aspect ratio match the correct
                  rotated rectangle's as much as possible.
        !*/</font>

        rectangle <b><a name='operator'></a>operator</b><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font> <font face='Lucida Console'>(</font>
            <font color='#0000FF'>const</font> rectangle<font color='#5555FF'>&amp;</font> r
        <font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>;
        <font color='#009900'>/*!
            ensures
                - returns (*this)(drectangle(r))
        !*/</font>

        <font color='#0000FF'>const</font> point_transform_affine<font color='#5555FF'>&amp;</font> <b><a name='get_tform'></a>get_tform</b><font face='Lucida Console'>(</font>
        <font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>; 
        <font color='#009900'>/*!
            ensures
                - returns the affine transformation this object uses to transform rectangles.
        !*/</font>

    <b>}</b>;

    <font color='#0000FF'><u>void</u></font> <b><a name='serialize'></a>serialize</b>   <font face='Lucida Console'>(</font><font color='#0000FF'>const</font> rectangle_transform<font color='#5555FF'>&amp;</font> item, std::ostream<font color='#5555FF'>&amp;</font> out<font face='Lucida Console'>)</font>;
    <font color='#0000FF'><u>void</u></font> <b><a name='deserialize'></a>deserialize</b> <font face='Lucida Console'>(</font>rectangle_transform<font color='#5555FF'>&amp;</font> item, std::istream<font color='#5555FF'>&amp;</font> in<font face='Lucida Console'>)</font>;
    <font color='#009900'>/*!
        provides serialization support
    !*/</font>

<font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
    <font color='#0000FF'>class</font> <b><a name='point_transform_projective'></a>point_transform_projective</b>
    <b>{</b>
        <font color='#009900'>/*!
            WHAT THIS OBJECT REPRESENTS
                This is an object that takes 2D points or vectors and 
                applies a projective transformation to them.

            THREAD SAFETY
                It is safe for multiple threads to make concurrent accesses to this object
                without synchronization.
        !*/</font>

    <font color='#0000FF'>public</font>:

        <b><a name='point_transform_projective'></a>point_transform_projective</b> <font face='Lucida Console'>(</font>
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            ensures
                - This object will perform the identity transform.  That is, given a point
                  as input it will return the same point as output.
        !*/</font>

        <b><a name='point_transform_projective'></a>point_transform_projective</b> <font face='Lucida Console'>(</font>
            <font color='#0000FF'>const</font> matrix<font color='#5555FF'>&lt;</font><font color='#0000FF'><u>double</u></font>,<font color='#979000'>3</font>,<font color='#979000'>3</font><font color='#5555FF'>&gt;</font><font color='#5555FF'>&amp;</font> m
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            ensures
                - #get_m() == m
        !*/</font>

        <b><a name='point_transform_projective'></a>point_transform_projective</b> <font face='Lucida Console'>(</font>
            <font color='#0000FF'>const</font> point_transform_affine<font color='#5555FF'>&amp;</font> tran
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            ensures
                - This object will perform exactly the same transformation as the given
                  affine transform.
        !*/</font>

        <font color='#0000FF'>const</font> dlib::vector<font color='#5555FF'>&lt;</font><font color='#0000FF'><u>double</u></font>,<font color='#979000'>2</font><font color='#5555FF'>&gt;</font> <b><a name='operator'></a>operator</b><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font> <font face='Lucida Console'>(</font>
            <font color='#0000FF'>const</font> dlib::vector<font color='#5555FF'>&lt;</font><font color='#0000FF'><u>double</u></font>,<font color='#979000'>2</font><font color='#5555FF'>&gt;</font><font color='#5555FF'>&amp;</font> p
        <font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>;
        <font color='#009900'>/*!
            ensures
                - Applies the projective transformation defined by this object's constructor
                  to p and returns the result.  To define this precisely:
                    - let p_h == the point p in homogeneous coordinates.  That is:
                        - p_h.x() == p.x()
                        - p_h.y() == p.y()
                        - p_h.z() == 1 
                    - let x == get_m()*p_h 
                    - Then this function returns the value x/x.z()
        !*/</font>

        <font color='#0000FF'>const</font> matrix<font color='#5555FF'>&lt;</font><font color='#0000FF'><u>double</u></font>,<font color='#979000'>3</font>,<font color='#979000'>3</font><font color='#5555FF'>&gt;</font><font color='#5555FF'>&amp;</font> <b><a name='get_m'></a>get_m</b><font face='Lucida Console'>(</font>
        <font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>;
        <font color='#009900'>/*!
            ensures
                - returns the transformation matrix used by this object.
        !*/</font>

    <b>}</b>;

    <font color='#0000FF'><u>void</u></font> <b><a name='serialize'></a>serialize</b>   <font face='Lucida Console'>(</font><font color='#0000FF'>const</font> point_transform_projective<font color='#5555FF'>&amp;</font> item, std::ostream<font color='#5555FF'>&amp;</font> out<font face='Lucida Console'>)</font>;
    <font color='#0000FF'><u>void</u></font> <b><a name='deserialize'></a>deserialize</b> <font face='Lucida Console'>(</font>point_transform_projective<font color='#5555FF'>&amp;</font> item, std::istream<font color='#5555FF'>&amp;</font> in<font face='Lucida Console'>)</font>;
    <font color='#009900'>/*!
        provides serialization support
    !*/</font>

<font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
    point_transform_projective <b><a name='operator'></a>operator</b><font color='#5555FF'>*</font> <font face='Lucida Console'>(</font>
        <font color='#0000FF'>const</font> point_transform_projective<font color='#5555FF'>&amp;</font> lhs,
        <font color='#0000FF'>const</font> point_transform_projective<font color='#5555FF'>&amp;</font> rhs
    <font face='Lucida Console'>)</font>;
    <font color='#009900'>/*!
        ensures
            - returns a transformation TFORM(x) that is equivalent to lhs(rhs(x)).  That
              is, for all valid x: TFORM(x) == lhs(rhs(x)).
    !*/</font>

<font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
    point_transform_projective <b><a name='inv'></a>inv</b> <font face='Lucida Console'>(</font>
        <font color='#0000FF'>const</font> point_transform_projective<font color='#5555FF'>&amp;</font> trans
    <font face='Lucida Console'>)</font>;
    <font color='#009900'>/*!
        ensures
            - If trans is an invertible transformation then this function returns a new
              transformation that is the inverse of trans. 
    !*/</font>

<font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
    point_transform_projective <b><a name='find_projective_transform'></a>find_projective_transform</b> <font face='Lucida Console'>(</font>
        <font color='#0000FF'>const</font> std::vector<font color='#5555FF'>&lt;</font>dlib::vector<font color='#5555FF'>&lt;</font><font color='#0000FF'><u>double</u></font>,<font color='#979000'>2</font><font color='#5555FF'>&gt;</font> <font color='#5555FF'>&gt;</font><font color='#5555FF'>&amp;</font> from_points,
        <font color='#0000FF'>const</font> std::vector<font color='#5555FF'>&lt;</font>dlib::vector<font color='#5555FF'>&lt;</font><font color='#0000FF'><u>double</u></font>,<font color='#979000'>2</font><font color='#5555FF'>&gt;</font> <font color='#5555FF'>&gt;</font><font color='#5555FF'>&amp;</font> to_points
    <font face='Lucida Console'>)</font>;
    <font color='#009900'>/*!
        requires
            - from_points.size() == to_points.size()
            - from_points.size() &gt;= 4
        ensures
            - returns a point_transform_projective object, T, such that for all valid i:
                length(T(from_points[i]) - to_points[i])
              is minimized as often as possible.  That is, this function finds the projective
              transform that maps points in from_points to points in to_points.  If no
              projective transform exists which performs this mapping exactly then the one
              which minimizes the mean squared error is selected. 
    !*/</font>

<font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
    <font color='#0000FF'>class</font> <b><a name='point_transform'></a>point_transform</b>
    <b>{</b>
        <font color='#009900'>/*!
            WHAT THIS OBJECT REPRESENTS
                This is an object that takes 2D points or vectors and 
                rotates them around the origin by a given angle and then
                translates them.

            THREAD SAFETY
                It is safe for multiple threads to make concurrent accesses to this object
                without synchronization.
        !*/</font>
    <font color='#0000FF'>public</font>:

        <b><a name='point_transform'></a>point_transform</b> <font face='Lucida Console'>(</font>
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            ensures
                - This object will perform the identity transform.  That is, given a point
                  as input it will return the same point as output.
        !*/</font>

        <b><a name='point_transform'></a>point_transform</b> <font face='Lucida Console'>(</font>
            <font color='#0000FF'>const</font> <font color='#0000FF'><u>double</u></font><font color='#5555FF'>&amp;</font> angle,
            <font color='#0000FF'>const</font> dlib::vector<font color='#5555FF'>&lt;</font><font color='#0000FF'><u>double</u></font>,<font color='#979000'>2</font><font color='#5555FF'>&gt;</font><font color='#5555FF'>&amp;</font> translate
        <font face='Lucida Console'>)</font>
        <font color='#009900'>/*!
            ensures
                - When (*this)(p) is invoked it will return a point P such that:
                    - P is the point p rotated counter-clockwise around the origin 
                      angle radians and then shifted by having translate added to it.
                      (Note that this is counter clockwise with respect to the normal
                      coordinate system with positive y going up and positive x going
                      to the right)
        !*/</font>

        <font color='#0000FF'>template</font> <font color='#5555FF'>&lt;</font><font color='#0000FF'>typename</font> T<font color='#5555FF'>&gt;</font>
        <font color='#0000FF'>const</font> dlib::vector<font color='#5555FF'>&lt;</font>T,<font color='#979000'>2</font><font color='#5555FF'>&gt;</font> <b><a name='operator'></a>operator</b><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font> <font face='Lucida Console'>(</font>
            <font color='#0000FF'>const</font> dlib::vector<font color='#5555FF'>&lt;</font>T,<font color='#979000'>2</font><font color='#5555FF'>&gt;</font><font color='#5555FF'>&amp;</font> p
        <font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>;
        <font color='#009900'>/*!
            ensures
                - rotates p, then translates it and returns the result.  The output
                  of this function is therefore equal to get_m()*p + get_b().
        !*/</font>

        <font color='#0000FF'>const</font> matrix<font color='#5555FF'>&lt;</font><font color='#0000FF'><u>double</u></font>,<font color='#979000'>2</font>,<font color='#979000'>2</font><font color='#5555FF'>&gt;</font> <b><a name='get_m'></a>get_m</b><font face='Lucida Console'>(</font>
        <font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>;
        <font color='#009900'>/*!
            ensures
                - returns the transformation matrix used by this object.
        !*/</font>

        <font color='#0000FF'>const</font> dlib::vector<font color='#5555FF'>&lt;</font><font color='#0000FF'><u>double</u></font>,<font color='#979000'>2</font><font color='#5555FF'>&gt;</font> <b><a name='get_b'></a>get_b</b><font face='Lucida Console'>(</font>
        <font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>;
        <font color='#009900'>/*!
            ensures
                - returns the offset vector used by this object.
        !*/</font>

    <b>}</b>;

    <font color='#0000FF'><u>void</u></font> <b><a name='serialize'></a>serialize</b>   <font face='Lucida Console'>(</font><font color='#0000FF'>const</font> point_transform<font color='#5555FF'>&amp;</font> item, std::ostream<font color='#5555FF'>&amp;</font> out<font face='Lucida Console'>)</font>;
    <font color='#0000FF'><u>void</u></font> <b><a name='deserialize'></a>deserialize</b> <font face='Lucida Console'>(</font>point_transform<font color='#5555FF'>&amp;</font> item, std::istream<font color='#5555FF'>&amp;</font> in<font face='Lucida Console'>)</font>;
    <font color='#009900'>/*!
        provides serialization support
    !*/</font>

<font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
    <font color='#0000FF'>class</font> <b><a name='point_rotator'></a>point_rotator</b>
    <b>{</b>
        <font color='#009900'>/*!
            WHAT THIS OBJECT REPRESENTS
                This is an object that takes 2D points or vectors and 
                rotates them around the origin by a given angle.

            THREAD SAFETY
                It is safe for multiple threads to make concurrent accesses to this object
                without synchronization.
        !*/</font>
    <font color='#0000FF'>public</font>:

        <b><a name='point_rotator'></a>point_rotator</b> <font face='Lucida Console'>(</font>
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            ensures
                - This object will perform the identity transform.  That is, given a point
                  as input it will return the same point as output.
        !*/</font>

        <b><a name='point_rotator'></a>point_rotator</b> <font face='Lucida Console'>(</font>
            <font color='#0000FF'>const</font> <font color='#0000FF'><u>double</u></font><font color='#5555FF'>&amp;</font> angle
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            ensures
                - When (*this)(p) is invoked it will return a point P such that:
                    - P is the point p rotated counter-clockwise around the origin 
                      angle radians.
                      (Note that this is counter clockwise with respect to the normal
                      coordinate system with positive y going up and positive x going
                      to the right)
        !*/</font>

        <font color='#0000FF'>template</font> <font color='#5555FF'>&lt;</font><font color='#0000FF'>typename</font> T<font color='#5555FF'>&gt;</font>
        <font color='#0000FF'>const</font> dlib::vector<font color='#5555FF'>&lt;</font>T,<font color='#979000'>2</font><font color='#5555FF'>&gt;</font> <b><a name='operator'></a>operator</b><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font> <font face='Lucida Console'>(</font>
            <font color='#0000FF'>const</font> dlib::vector<font color='#5555FF'>&lt;</font>T,<font color='#979000'>2</font><font color='#5555FF'>&gt;</font><font color='#5555FF'>&amp;</font> p
        <font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>;
        <font color='#009900'>/*!
            ensures
                - rotates p and returns the result. The output of this function is
                  therefore equal to get_m()*p.
        !*/</font>

        <font color='#0000FF'>const</font> matrix<font color='#5555FF'>&lt;</font><font color='#0000FF'><u>double</u></font>,<font color='#979000'>2</font>,<font color='#979000'>2</font><font color='#5555FF'>&gt;</font> <b><a name='get_m'></a>get_m</b><font face='Lucida Console'>(</font>
        <font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>;
        <font color='#009900'>/*!
            ensures
                - returns the transformation matrix used by this object.
        !*/</font>
    <b>}</b>;

    <font color='#0000FF'><u>void</u></font> <b><a name='serialize'></a>serialize</b>   <font face='Lucida Console'>(</font><font color='#0000FF'>const</font> point_rotator<font color='#5555FF'>&amp;</font> item, std::ostream<font color='#5555FF'>&amp;</font> out<font face='Lucida Console'>)</font>;
    <font color='#0000FF'><u>void</u></font> <b><a name='deserialize'></a>deserialize</b> <font face='Lucida Console'>(</font>point_rotator<font color='#5555FF'>&amp;</font> item, std::istream<font color='#5555FF'>&amp;</font> in<font face='Lucida Console'>)</font>;
    <font color='#009900'>/*!
        provides serialization support
    !*/</font>

<font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
    <font color='#0000FF'>template</font> <font color='#5555FF'>&lt;</font><font color='#0000FF'>typename</font> T<font color='#5555FF'>&gt;</font>
    <font color='#0000FF'>const</font> dlib::vector<font color='#5555FF'>&lt;</font>T,<font color='#979000'>2</font><font color='#5555FF'>&gt;</font> <b><a name='rotate_point'></a>rotate_point</b> <font face='Lucida Console'>(</font>
        <font color='#0000FF'>const</font> dlib::vector<font color='#5555FF'>&lt;</font>T,<font color='#979000'>2</font><font color='#5555FF'>&gt;</font> center,
        <font color='#0000FF'>const</font> dlib::vector<font color='#5555FF'>&lt;</font>T,<font color='#979000'>2</font><font color='#5555FF'>&gt;</font> p,
        <font color='#0000FF'><u>double</u></font> angle
    <font face='Lucida Console'>)</font>;
    <font color='#009900'>/*!
        ensures
            - returns a point P such that:
                - P is the point p rotated counter-clockwise around the given
                  center point by angle radians.
                  (Note that this is counter clockwise with respect to the normal
                  coordinate system with positive y going up and positive x going
                  to the right)
    !*/</font>

<font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
    matrix<font color='#5555FF'>&lt;</font><font color='#0000FF'><u>double</u></font>,<font color='#979000'>2</font>,<font color='#979000'>2</font><font color='#5555FF'>&gt;</font> <b><a name='rotation_matrix'></a>rotation_matrix</b> <font face='Lucida Console'>(</font>
         <font color='#0000FF'><u>double</u></font> angle
    <font face='Lucida Console'>)</font>;
    <font color='#009900'>/*!
        ensures
            - returns a rotation matrix which rotates points around the origin in a
              counter-clockwise direction by angle radians.
              (Note that this is counter clockwise with respect to the normal
              coordinate system with positive y going up and positive x going
              to the right)
              Or in other words, this function returns a matrix M such that, given a
              point P, M*P gives a point which is P rotated by angle radians around
              the origin in a counter-clockwise direction.
    !*/</font>

<font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
    <font color='#0000FF'>class</font> <b><a name='point_transform_affine3d'></a>point_transform_affine3d</b>
    <b>{</b>
        <font color='#009900'>/*!
            WHAT THIS OBJECT REPRESENTS
                This is an object that takes 3D points or vectors and 
                applies an affine transformation to them.

            THREAD SAFETY
                It is safe for multiple threads to make concurrent accesses to this object
                without synchronization.
        !*/</font>
    <font color='#0000FF'>public</font>:

        <b><a name='point_transform_affine3d'></a>point_transform_affine3d</b> <font face='Lucida Console'>(</font>
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            ensures
                - This object will perform the identity transform.  That is, given a point
                  as input it will return the same point as output.
        !*/</font>

        <b><a name='point_transform_affine3d'></a>point_transform_affine3d</b> <font face='Lucida Console'>(</font>
            <font color='#0000FF'>const</font> matrix<font color='#5555FF'>&lt;</font><font color='#0000FF'><u>double</u></font>,<font color='#979000'>3</font>,<font color='#979000'>3</font><font color='#5555FF'>&gt;</font><font color='#5555FF'>&amp;</font> m,
            <font color='#0000FF'>const</font> dlib::vector<font color='#5555FF'>&lt;</font><font color='#0000FF'><u>double</u></font>,<font color='#979000'>3</font><font color='#5555FF'>&gt;</font><font color='#5555FF'>&amp;</font> b
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            ensures
                - #get_m() == m
                - #get_b() == b
                - When (*this)(p) is invoked it will return a point P such that:
                    - P == m*p + b
        !*/</font>

        <font color='#0000FF'>const</font> dlib::vector<font color='#5555FF'>&lt;</font><font color='#0000FF'><u>double</u></font>,<font color='#979000'>3</font><font color='#5555FF'>&gt;</font> <b><a name='operator'></a>operator</b><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font> <font face='Lucida Console'>(</font>
            <font color='#0000FF'>const</font> dlib::vector<font color='#5555FF'>&lt;</font><font color='#0000FF'><u>double</u></font>,<font color='#979000'>3</font><font color='#5555FF'>&gt;</font><font color='#5555FF'>&amp;</font> p
        <font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>;
        <font color='#009900'>/*!
            ensures
                - applies the affine transformation defined by this object's constructor
                  to p and returns the result.
        !*/</font>

        <font color='#0000FF'>const</font> matrix<font color='#5555FF'>&lt;</font><font color='#0000FF'><u>double</u></font>,<font color='#979000'>3</font>,<font color='#979000'>3</font><font color='#5555FF'>&gt;</font><font color='#5555FF'>&amp;</font> <b><a name='get_m'></a>get_m</b><font face='Lucida Console'>(</font>
        <font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>;
        <font color='#009900'>/*!
            ensures
                - returns the transformation matrix used by this object.
        !*/</font>

        <font color='#0000FF'>const</font> dlib::vector<font color='#5555FF'>&lt;</font><font color='#0000FF'><u>double</u></font>,<font color='#979000'>3</font><font color='#5555FF'>&gt;</font><font color='#5555FF'>&amp;</font> <b><a name='get_b'></a>get_b</b><font face='Lucida Console'>(</font>
        <font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>;
        <font color='#009900'>/*!
            ensures
                - returns the offset vector used by this object.
        !*/</font>

    <b>}</b>;

    <font color='#0000FF'><u>void</u></font> <b><a name='serialize'></a>serialize</b>   <font face='Lucida Console'>(</font><font color='#0000FF'>const</font> point_transform_affine3d<font color='#5555FF'>&amp;</font> item, std::ostream<font color='#5555FF'>&amp;</font> out<font face='Lucida Console'>)</font>;
    <font color='#0000FF'><u>void</u></font> <b><a name='deserialize'></a>deserialize</b> <font face='Lucida Console'>(</font>point_transform_affine3d<font color='#5555FF'>&amp;</font> item, std::istream<font color='#5555FF'>&amp;</font> in<font face='Lucida Console'>)</font>;
    <font color='#009900'>/*!
        provides serialization support
    !*/</font>

<font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
    point_transform_affine3d <b><a name='operator'></a>operator</b><font color='#5555FF'>*</font> <font face='Lucida Console'>(</font>
        <font color='#0000FF'>const</font> point_transform_affine3d<font color='#5555FF'>&amp;</font> lhs,
        <font color='#0000FF'>const</font> point_transform_affine3d<font color='#5555FF'>&amp;</font> rhs
    <font face='Lucida Console'>)</font>;
    <font color='#009900'>/*!
        ensures
            - returns a transformation TFORM(x) that is equivalent to lhs(rhs(x)).  That
              is, for all valid x: TFORM(x) == lhs(rhs(x)).
    !*/</font>

<font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
    point_transform_affine3d <b><a name='operator'></a>operator</b><font color='#5555FF'>*</font> <font face='Lucida Console'>(</font>
        <font color='#0000FF'>const</font> point_transform_affine3d<font color='#5555FF'>&amp;</font> lhs,
        <font color='#0000FF'>const</font> point_transform_affine<font color='#5555FF'>&amp;</font> rhs
    <font face='Lucida Console'>)</font>;
    <font color='#009900'>/*!
        ensures
            - returns a transformation TFORM(x) that is equivalent to lhs(rhs(x)).  That
              is, for all valid x: TFORM(x) == lhs(rhs(x)).
    !*/</font>

<font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
    point_transform_affine3d <b><a name='inv'></a>inv</b> <font face='Lucida Console'>(</font>
        <font color='#0000FF'>const</font> point_transform_affine3d<font color='#5555FF'>&amp;</font> trans
    <font face='Lucida Console'>)</font>;
    <font color='#009900'>/*!
        ensures
            - If trans is an invertible transformation then this function returns a new
              transformation that is the inverse of trans. 
    !*/</font>

<font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
    point_transform_affine3d <b><a name='rotate_around_x'></a>rotate_around_x</b> <font face='Lucida Console'>(</font>
        <font color='#0000FF'><u>double</u></font> angle
    <font face='Lucida Console'>)</font>;
    <font color='#009900'>/*!
        ensures
            - Returns a transformation that rotates a point around the x axis in a
              counter-clockwise direction by angle radians.  That is, the rotation appears
              counter-clockwise when the x axis points toward the observer, the coordinate
              system is right-handed, and the angle is positive.
    !*/</font>

<font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
    point_transform_affine3d <b><a name='rotate_around_y'></a>rotate_around_y</b> <font face='Lucida Console'>(</font>
        <font color='#0000FF'><u>double</u></font> angle
    <font face='Lucida Console'>)</font>;
    <font color='#009900'>/*!
        ensures
            - Returns a transformation that rotates a point around the y axis in a
              counter-clockwise direction by angle radians.  That is, the rotation appears
              counter-clockwise when the y axis points toward the observer, the coordinate
              system is right-handed, and the angle is positive.
    !*/</font>

<font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
    point_transform_affine3d <b><a name='rotate_around_z'></a>rotate_around_z</b> <font face='Lucida Console'>(</font>
        <font color='#0000FF'><u>double</u></font> angle
    <font face='Lucida Console'>)</font>;
    <font color='#009900'>/*!
        ensures
            - Returns a transformation that rotates a point around the z axis in a
              counter-clockwise direction by angle radians.  That is, the rotation appears
              counter-clockwise when the z axis points toward the observer, the coordinate
              system is right-handed, and the angle is positive.
    !*/</font>

<font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
    point_transform_affine3d <b><a name='translate_point'></a>translate_point</b> <font face='Lucida Console'>(</font>
        <font color='#0000FF'>const</font> vector<font color='#5555FF'>&lt;</font><font color='#0000FF'><u>double</u></font>,<font color='#979000'>3</font><font color='#5555FF'>&gt;</font><font color='#5555FF'>&amp;</font> delta
    <font face='Lucida Console'>)</font>;
    <font color='#009900'>/*!
        ensures
            - returns a transformation that simply translates points by adding delta to
              them.  That is, this function returns:
                point_transform_affine3d(identity_matrix&lt;double&gt;(3),delta);
    !*/</font>

    point_transform_affine3d <b><a name='translate_point'></a>translate_point</b> <font face='Lucida Console'>(</font>
        <font color='#0000FF'><u>double</u></font> x,
        <font color='#0000FF'><u>double</u></font> y,
        <font color='#0000FF'><u>double</u></font> z
    <font face='Lucida Console'>)</font>;
    <font color='#009900'>/*!
        ensures
            - returns translate_point(vector&lt;double&gt;(x,y,z))
    !*/</font>

<font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
    <font color='#0000FF'>class</font> <b><a name='camera_transform'></a>camera_transform</b>
    <b>{</b>
        <font color='#009900'>/*!
            WHAT THIS OBJECT REPRESENTS
                This object maps 3D points into the image plane of a camera.  Therefore,
                you can use it to compute 2D representations of 3D data from the point of
                view of some camera in 3D space.

            THREAD SAFETY
                It is safe for multiple threads to make concurrent accesses to this object
                without synchronization.
        !*/</font>

    <font color='#0000FF'>public</font>:

        <b><a name='camera_transform'></a>camera_transform</b>  <font face='Lucida Console'>(</font>
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            ensures
                - #get_camera_pos()           == vector&lt;double&gt;(1,1,1) 
                - #get_camera_looking_at()    == vector&lt;double&gt;(0,0,0) 
                - #get_camera_up_direction()  == vector&lt;double&gt;(0,0,1) 
                - #get_camera_field_of_view() == 90
                - #get_num_pixels()           == 1 
        !*/</font>

        <b><a name='camera_transform'></a>camera_transform</b> <font face='Lucida Console'>(</font>
            <font color='#0000FF'>const</font> vector<font color='#5555FF'>&lt;</font><font color='#0000FF'><u>double</u></font><font color='#5555FF'>&gt;</font><font color='#5555FF'>&amp;</font> camera_pos,
            <font color='#0000FF'>const</font> vector<font color='#5555FF'>&lt;</font><font color='#0000FF'><u>double</u></font><font color='#5555FF'>&gt;</font><font color='#5555FF'>&amp;</font> camera_looking_at,
            <font color='#0000FF'>const</font> vector<font color='#5555FF'>&lt;</font><font color='#0000FF'><u>double</u></font><font color='#5555FF'>&gt;</font><font color='#5555FF'>&amp;</font> camera_up_direction,
            <font color='#0000FF'>const</font> <font color='#0000FF'><u>double</u></font> camera_field_of_view, 
            <font color='#0000FF'>const</font> <font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font> num_pixels
        <font face='Lucida Console'>)</font>;
        <font color='#009900'>/*!
            requires
                - 0 &lt; camera_field_of_view &lt; 180
            ensures
                - #get_camera_pos() == camera_pos
                - #get_camera_looking_at() == camera_looking_at
                - #get_camera_up_direction() == camera_up_direction
                - #get_camera_field_of_view() == camera_field_of_view
                - #get_num_pixels() == num_pixels
        !*/</font>

        dpoint <b><a name='operator'></a>operator</b><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font> <font face='Lucida Console'>(</font>
            <font color='#0000FF'>const</font> vector<font color='#5555FF'>&lt;</font><font color='#0000FF'><u>double</u></font><font color='#5555FF'>&gt;</font><font color='#5555FF'>&amp;</font> p
        <font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>;
        <font color='#009900'>/*!
            ensures
                - Maps the given 3D point p into the 2D image plane defined by the camera
                  parameters given to this object's constructor.  The 2D point in the image
                  plane is returned.
        !*/</font>

        dpoint <b><a name='operator'></a>operator</b><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font> <font face='Lucida Console'>(</font>
            <font color='#0000FF'>const</font> vector<font color='#5555FF'>&lt;</font><font color='#0000FF'><u>double</u></font><font color='#5555FF'>&gt;</font><font color='#5555FF'>&amp;</font> p,
            <font color='#0000FF'><u>double</u></font><font color='#5555FF'>&amp;</font> scale,
            <font color='#0000FF'><u>double</u></font><font color='#5555FF'>&amp;</font> distance
        <font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>;
        <font color='#009900'>/*!
            ensures
                - Maps the given 3D point p into the 2D image plane defined by the camera
                  parameters given to this object's constructor.  The 2D point in the image
                  plane is returned.
                - #scale == a number that tells you how large things are at the point p.
                  Objects further from the camera appear smaller, in particular, they
                  appear #scale times their normal size.
                - #distance == how far away the point is from the image plane.  Objects in
                  front of the camera will have a positive distance and those behind a
                  negative distance.
        !*/</font>

        vector<font color='#5555FF'>&lt;</font><font color='#0000FF'><u>double</u></font><font color='#5555FF'>&gt;</font> <b><a name='get_camera_pos'></a>get_camera_pos</b><font face='Lucida Console'>(</font>
        <font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>;
        <font color='#009900'>/*!
            ensures
                - returns the position, in 3D space, of the camera.  When operator() is
                  invoked it maps 3D points into the image plane of this camera.
        !*/</font>

        vector<font color='#5555FF'>&lt;</font><font color='#0000FF'><u>double</u></font><font color='#5555FF'>&gt;</font> <b><a name='get_camera_looking_at'></a>get_camera_looking_at</b><font face='Lucida Console'>(</font>
        <font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>;
        <font color='#009900'>/*!
            ensures
                - returns the point in 3D space the camera is pointed at.  
        !*/</font>

        vector<font color='#5555FF'>&lt;</font><font color='#0000FF'><u>double</u></font><font color='#5555FF'>&gt;</font> <b><a name='get_camera_up_direction'></a>get_camera_up_direction</b><font face='Lucida Console'>(</font>
        <font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>;
        <font color='#009900'>/*!
            ensures
                - returns a vector that defines what direction is "up" for the camera.
                  This means that as you travel from the bottom of the image plane to the
                  top you will be traveling in the direction of this vector.  Note that
                  get_camera_up_direction() doesn't need to be orthogonal to the camera's
                  line of sight (i.e. get_camera_looking_at()-get_camera_pos()), it just
                  needs to not be an exact multiple of the line of sight.  Any necessary
                  orthogonalization will be taken care of internally.
        !*/</font>

        <font color='#0000FF'><u>double</u></font> <b><a name='get_camera_field_of_view'></a>get_camera_field_of_view</b><font face='Lucida Console'>(</font>
        <font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>;
        <font color='#009900'>/*!
            ensures
                - returns the field of view of the camera in degrees.
        !*/</font>

        <font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font> <b><a name='get_num_pixels'></a>get_num_pixels</b><font face='Lucida Console'>(</font>
        <font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>;
        <font color='#009900'>/*!
            ensures
                - 3D points that fall within the field of view of the camera are mapped by
                  operator() into the pixel coordinates of a get_num_pixels() by
                  get_num_pixels() image.  Therefore, you can use the output of operator()
                  to index into an image.  However, you still need to perform bounds
                  checking as there might be 3D points outside the field of view of the
                  camera and those will be mapped to 2D points outside the image.
        !*/</font>

    <b>}</b>;

    <font color='#0000FF'><u>void</u></font> <b><a name='serialize'></a>serialize</b>   <font face='Lucida Console'>(</font><font color='#0000FF'>const</font> camera_transform<font color='#5555FF'>&amp;</font> item, std::ostream<font color='#5555FF'>&amp;</font> out<font face='Lucida Console'>)</font>;
    <font color='#0000FF'><u>void</u></font> <b><a name='deserialize'></a>deserialize</b> <font face='Lucida Console'>(</font>camera_transform<font color='#5555FF'>&amp;</font> item, std::istream<font color='#5555FF'>&amp;</font> in<font face='Lucida Console'>)</font>;
    <font color='#009900'>/*!
        provides serialization support
    !*/</font>

<font color='#009900'>// ----------------------------------------------------------------------------------------
</font>
<b>}</b>

<font color='#0000FF'>#endif</font> <font color='#009900'>// DLIB_POINT_TrANSFORMS_ABSTRACT_Hh_
</font>


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